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Gerstner waves and their generalizations in hydrodynamics and geophysics

 a, b,  a, c, b
a Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
b National Research University Higher School of Economics, Nizhny Novgorod Branch, B. Pecherskaya str. 25/12, Nizhny Novgorod, 603155, Russian Federation
c Alexeev Nizhnii Novgorod State Technical University, Minina str. 24, Nizhnii Novgorod, 603600, Russian Federation

An overview of exact solutions for water waves is given, each of which is a generalization of the Gerstner wave. Additional factors are coastal geometry, fluid rotation, unstable pressure on the free surface, stratification, fluid compressibility, and background flows. Waves on a rotating Earth are studied in the f-plane approximation, and in the near-equatorial region also in the β-plane approximation. The flows are described in Lagrangian variables. For all waves in the absence of background flows, the trajectories of liquid particles are circles, as in the Gerstner wave (hence their common name - Gerstner-like).

Keywords: Gerstner waves, Lagrangian coordinates, vorticity, Cauchy invariants, edge waves, Ptolemaic flows, rotating fluid, f - plane approximation, equatorially trapped waves
PACS: 47.35.Bb
DOI: 10.3367/UFNe.2021.05.038980
Citation: Abrashkin A A, Pelinovsky E N "Gerstner waves and their generalizations in hydrodynamics and geophysics" Phys. Usp., accepted

Received: 1st, February 2021, revised: 9th, April 2021, 3rd, May 2021

Оригинал: Абрашкин А А, Пелиновский Е Н «Волны Герстнера и их обобщения в гидродинамике и геофизике» УФН, принята к публикации; DOI: 10.3367/UFNr.2021.05.038980

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